How can I skip the long-time connection check?
I don't waiting, I want go in career mode immediately

Why would you want to do that? This year its worth connecting to EA servers,due to Football Club and all.
But being a web programmer, your question whetted my curiosity.So i sat down with my tools and 10 mins later i found out the answer for you
If you still want to do it.This is how to do it.
open the file
CWindows\System32\drivers\etc\hosts
You will have to open the file in notepad.
enter the following lines after the last line in the file

The lines in Green will stop your connection to Origin.So you can start Fifa without connecting to Origin.
The lines in red will stop Fifa from communicating to EA servers.
You can use one or both.Depends upon you.